Barnes copper bullets are designed for higher weight retention and deeper penetration. Being made out of one chunk of copper they aren't supposed to come apart (jacket seperated from lead core) when hitting something solid like a shoulder bone. But a solid copper bullet also wouldn't expand very much. Research came up with a method of manufacturing them to peel back into the four "petals" because there wasn't really any way of making them mushroom reliably, and the "X-bullet" was born. Being made out of solid copper, the interaction between the bullet and barrel was different than regular bullets, it required different loading techniques and there were/are claims of increased fouling. The Triple Shock took the X-Bullet and put grooves around the shank of the bullet, reducing the amount of contact between the bullet and barrel, thus reducing friction and fouling, and the possibility of increased velocity at the same or lower pressure.
The advertising for the Triple-Shock hypes three impacts (yeah right), first contact, the start of expansion, and full expansion of the "razor-sharp petals". Well, like most advertising claims, that's a little over the top. They are good bullets that penetrate deeply and hold together very well. Being a solid piece of metal, they are very stable in their rotation, but all premium bullets and most plain-jane bullets now have very concentric jackets and are well balanced bullets. The main thing is that they hold together while expanding reliably. The increase in penetration is due this. If a bullet breaks up, the loss of mass results in less momentum to keep the bullet moving through whatever it hits. As far as the razor sharp petals, it doesn't really matter if they are razor sharp or not. The petals increase the cutting/tearing as the bullet moves through the animal, probably very slightly more surface contact than a mushroomed conventional bullet, but due to their shape should "push" on through easier than a big flat surface.
I don't know what stores are getting for the Federal ammo loaded with the Barnes Triple Shock, I haven't bought any factory ammo for any of my rifles for years. I have tried some loads using X-Bullets in a couple of rifles and was thinking about working up a load with the Triple Shock for my .300 WSM Savage. We do have big deer, both muleys and whitetails here where I hunt in Nebraska, but neither the .300 or super premium bullets are required, and won't kill them any deader than my .270. As a comparison, I use 140 grain Nosler Ballistic Tips in my .270, a bullet that a lot of people say breaks up too easily and doesn't penetrate. All but one of the deer I've shot with it had exit holes, most showing good but not excessive expansion. The one that didn't exit probably wouldn't have no matter what bullet I was using (175 yds., steeply quartering toward me with a cross wind, hit about 2" to the left of point of aim,clipped 2 ribs, completely took out one lung, passed most of the way diagonally through the body and most of the bullet lodged in a partially destroyed far side hip, deer dropped on the spot, dead when I got to it.)